Specific gravity of soil: ASTM D854 test and formula

The specific gravity of soil, $G_s$, tells you how heavy the soil grains are compared with water. The specific gravity test, ASTM D854, measures it with a water pycnometer: you weigh a calibrated flask full of water, then the same flask with a known mass of dry soil and water, and the difference between the two weighings gives the volume of the grains. Soil classification doesn’t use $G_s$, but almost every phase relationship does: void ratio, porosity, degree of saturation, the zero air voids curve of a compaction test and the hydrometer analysis all need it.

Specific gravity calculator

The calculator also has a page of its own, to keep at hand: the specific gravity calculator.

What is the specific gravity of soil?

The specific gravity of soil solids is the mass of a volume of soil grains divided by the mass of the same volume of gas-free distilled water at the same temperature. Because it compares two masses, it has no units. Labs usually report it referred to water at 20 °C. Written with densities:

$$G_s = \frac{\rho_s}{\rho_w}$$

where $\rho_s$ is the density of the solid particles and $\rho_w$ the density of water. Multiplying $G_s$ by the density of water at 20 °C gives the density of the soil solids, which hardly changes with temperature.

The pycnometer test rests on Archimedes’ principle: the grains push out a volume of water equal to their own volume, and weighing that water gives the volume. Air trapped between the grains adds volume that isn’t soil, and a change in temperature changes how much water fits in the flask; most of the procedure is there to control those two.

ASTM D854 applies to the soil solids that pass a sieve. The 2014 edition tests the fraction passing the 4.75 mm (No. 4) sieve. The 2023 edition accepts solids passing the 9.5 mm (3/8 in.) sieve or a smaller one, and keeps the split on the No. 4 sieve as the referee method. The retained fraction is tested with ASTM C127, and the two results are combined (see the calculations). The method doesn’t suit solids that the test itself would change or highly organic material that floats in water; ASTM D5550, with a gas pycnometer, can be used for those. Soils with water-soluble matter, such as salt, or with added cement or lime need special treatment.

Specific gravity formula

In the pycnometer test, the densities in the definition become three masses. Call $M_{BW}$ the mass of the flask filled with water, and put a mass $M_s$ of dry soil into it. The soil pushes out a volume of water equal to the volume of the grains, $V_s$, so the flask with water and soil weighs:

$$M_{BWS} = M_{BW} + M_s - \rho_w V_s$$

Solving for the mass of the water the grains displaced, $\rho_w V_s = M_{BW} + M_s - M_{BWS}$, and dividing the mass of the grains by it gives the specific gravity formula of the pycnometer test:

$$G_T = \frac{M_s}{M_{BW} + M_s - M_{BWS}}$$

Where:
$G_T$ is the specific gravity of the soil solids at the test temperature $T$,
$M_s$ is the mass of the oven-dry soil, in g,
$M_{BW}$ is the mass of the flask filled with water to the calibration mark, at temperature $T$, in g,
$M_{BWS}$ is the mass of the flask filled with water and soil to the same mark, at temperature $T$, in g.

The denominator is the mass of the water that the grains displace. The same idea works for any solid: its specific gravity is its density divided by the density of water.

Specific gravity of water and the temperature correction

The specific gravity of water is 1 when it is compared with water at the same temperature. Its density does change with temperature, though: the calculator uses 0.99821 g/mL at 20 °C and 0.99705 g/mL at 25 °C. Two consequences follow for the test:

• $M_{BW}$ and $M_{BWS}$ must both be at the same temperature $T$. A flask that holds 250 mL of water at 20 °C holds about 0.3 g less water at 25 °C. With 30 g of soil displacing about 11 g of water, an error of 0.3 g in $M_{BW}$ moves $G_s$ by about 0.07.
• The result at the test temperature is referred to water at 20 °C with the temperature coefficient $K$, the specific gravity of water at $T$ relative to water at 20 °C:

$$K = \frac{\rho_w(T)}{\rho_w(20\,^\circ\mathrm{C})}, \qquad G_{20} = K \cdot G_T$$

At 25 °C, $K = 0.99705 / 0.99821 = 0.99884$. ASTM D854 tabulates $K$ against temperature; Caltrans CT 209 publishes a similar table.

Equipment

• Pycnometer: a stoppered flask, a stoppered iodine flask or a volumetric flask of at least 250 mL. Flasks of 250 mL and 500 mL are the usual sizes.
• Balance readable to 0.01 g, with a capacity of at least 500 g for a 250 mL pycnometer or at least 1,000 g for a 500 mL one.
• Drying oven that holds 110 ± 5 °C.
• Thermometer readable to 0.1 °C, with a maximum error of 0.5 °C, that can be read at an immersion depth between 25 and 80 mm.
• Desiccator with silica gel or anhydrous calcium sulfate, to cool the dried soil without it taking up moisture.
• A way to remove entrapped air: a vacuum pump or water aspirator that brings the absolute pressure below 100 mm Hg (13.33 kPa), or a hot plate or Bunsen burner that can keep water boiling.
• Insulated container with a lid, such as a foam cooler, big enough for three to six pycnometers plus a beaker or bottle of de-aired water, an eyedropper and the thermometer.
• Funnel of smooth, non-corrosive material, with a stem that reaches past the calibration mark or the stopper seat, and a filling tube with side vents, to add water without stirring up the slurry.
• Blender with mixing blades, to disperse moist specimens (Method A).
• No. 4 (4.75 mm) sieve, and the 9.5 mm sieve if you follow the 2023 edition’s split.
• Distilled water, de-aired for calibration and for topping up.
• Evaporating dish or pan large enough for the whole slurry.

Calibrating the pycnometer

The calibration gives the volume of the flask up to its mark. With that volume you can work out $M_{BW}$ at whatever temperature the test ends up at, without having to reach a set temperature.

With $V_B$ known, the mass of the pycnometer full of water at the test temperature $T$ is:

$$M_{BW} = M_B + V_B \, \rho_w(T)$$

Caltrans CT 209 writes the same correction in terms of masses, $M_{BW}(T) = \frac{\rho_w(T)}{\rho_w(T_c)}\left[M_{BW}(T_c) - M_B\right] + M_B$. The older USACE manual EM 1110-2-1906 instead weighs the flask with water at several temperatures and draws a calibration curve from which $M_{BW}$ is read at $T$. Any of the three gives $M_{BW}$ at the temperature of the test.

The calibration stays valid while the empty pycnometer keeps its mass. Before each test, weigh it on the same balance used for the calibration: if it differs from $M_B$ by more than 0.06 g, calibrate it again.

Pycnometer test procedure (ASTM D854)

Method A or Method B

ASTM D854 has two ways of preparing the specimen:

• Method A, with moist specimens, is the preferred method. It is required for organic soils, highly plastic fine-grained soils, tropical soils and soils containing halloysite, because oven-drying can alter some of these soils or make them hard to wet again.
• Method B, with oven-dried specimens, takes less time and suits clean sands.

In both methods the dry mass of the soil, $M_s$, is measured at the end of the test by drying the recovered slurry.

Specimen mass

The dry mass of the specimen depends on the soil type and on the size of the pycnometer (ASTM D854-14):

Soil type (USCS)	Dry mass, 250 mL pycnometer (g)	Dry mass, 500 mL pycnometer (g)
SP, SP-SM	60 ± 10	100 ± 10
SP-SC, SM, SC	45 ± 10	75 ± 10
Silt or clay	35 ± 10	50 ± 10

Method A: preparing a moist specimen

Method B: preparing an oven-dried specimen

Removing the entrapped air

Entrapped air is the main source of error in this test: a bubble left among the grains is counted as soil volume and lowers $G_s$. ASTM D854 removes it in one of these ways:

• Boiling for at least 2 hours, agitating the pycnometer from time to time.
• Vacuum for at least 2 hours, below 100 mm Hg absolute, agitating the pycnometer continuously.
• Boiling and vacuum together for at least 1 hour counted from when boiling starts, rolling the pycnometer now and then.

Under vacuum, a warm water bath no hotter than 40 °C helps the air come out; keep the bath level slightly below the water level inside the pycnometer. Watch the slurry while it boils, because a violent boil can throw soil out of the flask.

Filling, equilibrium and weighing

ASTM D854 calls for a single specimen. If you test a second one as a check, it is a complete test of its own, with its own de-airing and night of equilibrium.

Calculations

1. Mass of the dry soil:

   $$M_s = M_{sc} - M_c$$

   Where $M_s$ is the mass of the oven-dry soil, $M_{sc}$ the mass of the dish with the dry soil, and $M_c$ the mass of the empty dish, all in g.

2. Mass of the pycnometer full of water at the test temperature, from the calibration:

   $$M_{BW} = M_B + V_B \, \rho_w(T)$$

   The calculator takes $M_{BW}$ weighed at the test temperature $T$ or, switched to the calibration, works it out from $M_B$ and $V_B$.

3. Specific gravity at the test temperature:

   $$G_T = \frac{M_s}{M_{BW} + M_s - M_{BWS}}$$

4. Specific gravity at 20 °C:

   $$G_{20} = K \cdot G_T, \qquad K = \frac{\rho_w(T)}{\rho_w(20\,^\circ\mathrm{C})}$$

5. If the sample had particles retained on the dividing sieve, combine the specific gravity of the fine fraction (D854), $G_f$, with that of the coarse fraction (ASTM C127), $G_c$. The combination is made on the volume of the solids, which is what USACE EM 1110-2-1906 calls for:

   $$G_s = \frac{1}{\dfrac{P_f}{G_f} + \dfrac{P_c}{G_c}}$$

   Where $P_f$ and $P_c$ are the fractions of the total dry mass that pass and are retained on the dividing sieve, as decimals ($P_f + P_c = 1$). The calculator combines the two when you switch on the coarse fraction.

With the calculator’s example: the dish weighs $M_c = 278.2$ g and, with the dry soil, $M_{sc} = 307.8$ g, so $M_s = 29.6$ g. At $T = 20$ °C the pycnometer weighs $M_{BW} = 348.2$ g with water and $M_{BWS} = 366.8$ g with water and soil. The soil displaced $348.2 + 29.6 - 366.8 = 11.0$ g of water, so $G_T = 29.6 / 11.0 = 2.691$. At 20 °C, $K = 1$ and $G_{20} = 2.691$. Had the test run at 25 °C with the same masses, $G_{20} = 0.99884 \times 2.691 = 2.688$.

Report

• Identification of the sample and the fraction tested (the sieve it passes).
• Method used (A or B) and how the entrapped air was removed.
• Test temperature, $T$.
• Specific gravity at 20 °C, $G_{20}$. ASTM D854 sizes its balances, pycnometers and specimens so the result can be reported to four significant digits, for example 2.691.
• If the sample had a coarse fraction: its specific gravity by ASTM C127, the fractions $P_f$ and $P_c$, and the combined value.

Typical values and common mistakes

Most soils have a specific gravity between 2.60 and 2.80. Values from about 2.2 up to 3.5 are possible, but a result outside 2.60 to 2.80 calls for a second look at the test before it is accepted. Without a test, an FHWA research report takes 2.65 for sands and gravels and 2.78 for silts and clays. Organic matter, much lighter than mineral grains, pulls $G_s$ down; heavy minerals such as iron oxides push it up.

The usual causes of a wrong result:

• Air left in the slurry, usually from cutting the de-airing short. It gives a $G_s$ that is too low.
• $M_{BW}$ taken at a different temperature from $M_{BWS}$. Use the calibration to bring $M_{BW}$ to the test temperature.
• Soil lost while transferring it into the pycnometer, during boiling, or while washing it out into the dish.
• Water on the rim or the outside of the flask, or the water level off the mark, when weighing.
• A flask that has changed mass (chipped, or with residue) and was not calibrated again.

References

• ASTM International. ASTM D854-23, Standard Test Methods for Specific Gravity of Soil Solids by the Water Displacement Method. Scope and summary: store.astm.org/d0854-23.html.
• NICET (2020). Performance Examination checklist, ASTM D854-14 [AASHTO T 100]: nicet.org.
• California Department of Transportation (2011). California Test 209, Method of Test for Specific Gravity of Soils: dot.ca.gov.
• U.S. Army Corps of Engineers (1970, with changes to 1986). EM 1110-2-1906, Laboratory Soils Testing, Appendix IV: Specific Gravity.
• Hossain, M. S., Islam, M. A., Badhon, F. F., & Imtiaz, T. (2021). Properties and Behavior of Soil: Online Lab Manual, chapter 2, Specific Gravity Test. University of Texas at Arlington: uta.pressbooks.pub.
• Federal Highway Administration (2004). FHWA-HRT-04-094, Evaluation of LS-DYNA Soil Material Model 147, chapter 4: fhwa.dot.gov.
• Germaine, J. T., & Germaine, A. V. (2009). Geotechnical laboratory measurements for engineers.